Andrew Spakowitz, Postdoctoral Faculty Sponsor
Andrew Spakowitz, Postdoctoral Research Mentor
Importance of Many Particle Correlations to the Collective Debye-Waller Factor in a Single-Particle Activated Dynamic Theory of the Glass Transition.
The journal of physical chemistry. B
We theoretically study the importance of many body correlations on the collective Debye-Waller (DW) factor in the context of the Nonlinear Langevin Equation (NLE) single-particle activated dynamics theory of glass transition and its extension to include collective elasticity (ECNLE theory). This microscopic force-based approach envisions structural alpha relaxation as a coupled local-nonlocal process involving correlated local cage and longer range collective barriers. The crucial question addressed here is the importance of the deGennes narrowing contribution versus a literal Vineyard approximation for the collective DW factor that enters the construction of the dynamic free energy in NLE theory. While the Vineyard-deGennes approach-based NLE theory and its ECNLE theory extension yields predictions that agree well with experimental and simulation results, use of a literal Vineyard approximation for the collective DW factor massively overpredicts the activated relaxation time. The current study suggests many particle correlations are crucial for a reliable description of activated dynamics theory of model hard sphere fluids.
View details for DOI 10.1021/acs.jpcb.3c02089
View details for PubMedID 37229571
Microscopic activated dynamics theory of the shear rheology and stress overshoot in ultradense glass-forming fluids and colloidal suspensions
JOURNAL OF RHEOLOGY
2023; 67 (2): 559-578
View details for DOI 10.1122/8.0000546
View details for Web of Science ID 000936916500001
Semiflexible polymer solutions. II. Fluctuations and Frank elastic constants.
The Journal of chemical physics
2022; 157 (15): 154906
We study the collective elastic behavior of semiflexible polymer solutions in a nematic liquid-crystalline state using polymer field theory. Our polymer field-theoretic model of semiflexible polymer solutions is extended to include second-order fluctuation corrections to the free energy, permitting the evaluation of the Frank elastic constants based on orientational order fluctuations in the nematic state. Our exact treatment of wormlike chain statistics permits the evaluation of behavior from the nematic state, thus accurately capturing the impact of single-chain behavior on collective elastic response. Results for the Frank elastic constants are presented as a function of aligning field strength and chain length, and we explore the impact of conformation fluctuations and hairpin defects on the twist, splay, and bend moduli. Our results indicate that the twist elastic constant Ktwist is smaller than both bend and splay constants (Kbend and Ksplay, respectively) for the entire range of polymer rigidity. Splay and bend elastic constants exhibit regimes of dominance over the range of chain stiffness, where Ksplay > Kbend for flexible polymers (large-N limit) while the opposite is true for rigid polymers. Theoretical analysis also suggests the splay modulus tracks exactly to that of the end-to-end distance in the transverse direction for semiflexible polymers at intermediate to large-N. These results provide insight into the role of conformation fluctuations and hairpin defects on the collective response of polymer solutions.
View details for DOI 10.1063/5.0120526
View details for PubMedID 36272793
Active and thermal fluctuations in multi-scale polymer structure and dynamics.
The presence of athermal noise or biological fluctuations control and maintain crucial life-processes. In this work, we present an exact analytical treatment of the dynamic behavior of a flexible polymer chain that is subjected to both thermal and active forces. Our model for active forces incorporates temporal correlation associated with the characteristic time scale and processivity of enzymatic function (driven by ATP hydrolysis), leading to an active-force time scale that competes with relaxation processes within the polymer chain. We analyze the structure and dynamics of an active-Brownian polymer using our exact results for the dynamic structure factor and the looping time for the chain ends. The spectrum of relaxation times within a polymer chain implies two different behaviors at small and large length scales. Small length-scale relaxation is faster than the active-force time scale, and the dynamic and structural behavior at these scales are oblivious to active forces and, are thus governed by the true thermal temperature. Large length-scale behavior is governed by relaxation times that are much longer than the active-force time scale, resulting in an effective active-Brownian temperature that dramatically alters structural and dynamic behavior. These complex multi-scale effects imply a time-dependent temperature that governs living and non-equilibrium systems, serving as a unifying concept for interpreting and predicting their physical behavior.
View details for DOI 10.1039/d2sm00593j
View details for PubMedID 36000419
Influence of Attractive Functional Groups on the Segmental Dynamics and Glass Transition in Associating Polymers
2022; 55 (6): 2345–2357
View details for DOI 10.1021/acs.macromol.2c00080
Statistical behavior of nonequilibrium and living biological systems subjected to active and thermal fluctuations.
Physical review. E
2022; 105 (1-1): 014415
We present a path-integral formulation of the motion of a particle subjected to fluctuating active and thermal forces. This general framework predicts the statistical behavior associated with the stochastic trajectories of the particle, accounting for all possible realizations of Brownian and active forces, over an arbitrary potential landscape. Temporal correlations in the active forces result in non-Markovian statistics, necessitating the inclusion of a fixed active-force value at specified times within the statistical treatment. We specialize our theory to that of exponentially correlated active forces for a particle in a harmonic potential. We find the exact results for the statistical distributions for the initial position of the particle, accounting for the impact of the correlated active forces at all times prior to the initial time. Our theory is then used to find the two-point distribution for the active Brownian particle, which governs the joint probability that a particle begins and ends at specified locations. Analyses of the active Brownian statistics demonstrate that the impact of active forces can be interpreted through a time-dependent temperature whose influence depends on the competition of timescales of the active-force correlation and the relaxation time of the particle in the harmonic potential. The general results presented in this work are transferable to a broad range of nonequilibrium systems with active and Brownian motion, and the time-dependent temperature serves as a governing principle to describe the competition of timescales associated with active forces and internal relaxation processes.
View details for DOI 10.1103/PhysRevE.105.014415
View details for PubMedID 35193230
Linear and nonlinear viscoelasticity of concentrated thermoresponsive microgel suspensions
JOURNAL OF COLLOID AND INTERFACE SCIENCE
2021; 601: 886-898
We present an integrated experimental and theoretical study of the dynamics and rheology of self-crosslinked, slightly charged, temperature responsive soft poly(N-isopropylacrylamide) (pNIPAM) microgels over a wide range of concentration and temperature spanning the sharp change in particle size and intermolecular interactions across the lower critical solution temperature (LCST). Dramatic, non-monotonic changes in viscoelasticity are observed as a function of temperature, with distinct concentration dependence in the dense fluid, glassy, and soft-jammed regimes. Motivated by our experimental observations, we formulate a minimalistic model for the size dependence of a single microgel particle and the change of the interparticle interaction from purely repulsive to attractive upon heating. Using microscopic equilibrium and time-dependent statistical mechanical theories, theoretical predictions are quantitatively compared with experimental measurements of the shear modulus. Good agreement is found for the nonmonotonic temperature behavior that originates as a consequence of the competition between reduced microgel packing fraction and increasing interparticle attractions. Testable predictions are made for nonlinear rheological properties such as the yield stress and strain. To our knowledge, this is the first attempt to quantitatively understand in a unified manner the viscoelasticity of dense, temperature-responsive microgel suspensions spanning a wide range of temperatures and concentrations.
View details for DOI 10.1016/j.jcis.2021.05.111
View details for Web of Science ID 000687288600006
View details for PubMedID 34186277
Physical Bond Breaking in Associating Copolymer Liquids
ACS MACRO LETTERS
2021; 10 (1): 122-128
View details for DOI 10.1021/acsmacrolett.0c00697
View details for Web of Science ID 000612355000017
The role of collective elasticity on activated structural relaxation, yielding, and steady state flow in hard sphere fluids and colloidal suspensions under strong deformation
JOURNAL OF CHEMICAL PHYSICS
2020; 153 (19): 194502
We theoretically study the effect of external deformation on activated structural relaxation and aspects of the nonlinear mechanical response of glassy hard sphere fluids in the context of elastically collective nonlinear Langevin equation theory. This microscopic force-based approach describes activated relaxation as a coupled local-nonlocal event involving caging and longer range collective elasticity, with the latter becoming more important and ultimately dominant with increasing packing fraction under equilibrium conditions. The central new question we address is how this physical picture of activated relaxation, and the relative importance of local caging vs collective elasticity physics, depends on external deformation. Theoretical predictions are presented for deformation-induced enhancement of mobility, the onset of relaxation speed up at remarkably low values of stress, strain, or shear rate, apparent power law thinning of the steady state structural relaxation time and viscosity, a non-vanishing activation barrier in the shear thinning regime, an apparent Herschel-Bulkley form of the rate dependence of the steady state shear stress, exponential growth of different measures of a dynamic yield or flow stress with the packing fraction, and reduced fragility and dynamic heterogeneity under deformation. The results are contrasted with experiments and simulations, and qualitative or better agreement is found. An overarching conclusion is that deformation strongly reduces the importance of longer range collective elastic effects relative to the local caging aspect for most, but not all, physical questions, with deformation-dependent fragility and dynamic heterogeneity phenomena being qualitatively sensitive to collective elasticity. Overall, nonlinear rheology is predicted to be a more local problem than quiescent structural relaxation, albeit with deformation-modified activated processes still important.
View details for DOI 10.1063/5.0026258
View details for Web of Science ID 000595279100001
View details for PubMedID 33218226
Microscopic Theory of the Effect of Caging and Physical Bonding on Segmental Relaxation in Associating Copolymer Liquids
2020; 53 (11): 4366-4380
View details for DOI 10.1021/acs.macromol.0c00415
View details for Web of Science ID 000541512200024
Microscopic theory of onset of decaging and bond-breaking activated dynamics in ultradense fluids with strong short-range attractions
Physical Review E
2020; 101: 060601(R)
View details for DOI 10.1103/PhysRevE.101.060601
Microscopic theory of the influence of strong attractive forces on the activated dynamics of dense glass and gel forming fluids
JOURNAL OF CHEMICAL PHYSICS
2019; 151 (24): 244502
We theoretically study the nonmonotonic (re-entrant) activated dynamics associated with a finite time scale kinetically defined repulsive glass to fluid to attractive glass transition in high volume fraction particle suspensions interacting via strong short range attractive forces. The classic theoretical "projection" approximation that replaces all microscopic forces by a single effective force determined solely by equilibrium pair correlations is revisited based on the "projectionless dynamic theory" (PDT). A hybrid-PDT approximation is formulated that explicitly quantifies how attractive forces induce dynamical constraints, while singular hard core interactions are treated based on the projection approach. Both the effects of interference between repulsive and attractive forces, and structural changes due to attraction-induced bond formation that competes with caging, are included. Combined with the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated relaxation, the resultant approach appears to properly capture both the re-entrant dynamic crossover behavior and the strong nonmonotonic variation of the activated structural relaxation time with attraction strength and range at very high volume fractions as observed experimentally and in simulations. Testable predictions are made. Major differences compared to both ideal mode coupling theory and ECNLE theory based on the full force projection approximation are identified. Calculations are also performed for smaller time and length scale intracage dynamics relevant to the non-Gaussian parameter based on analyzing the dynamic free energy that controls particle trajectories. Implications of the new theory for thermal glass forming liquids with relatively long range attractive forces are briefly analyzed.
View details for DOI 10.1063/1.5129941
View details for Web of Science ID 000513160200043
View details for PubMedID 31893898
Thermoresponsive Stiffening with Microgel Particles in a Semiflexible Fibrin Network
2019; 52 (8): 3029-3041
View details for DOI 10.1021/acs.macromol.9b00124
View details for Web of Science ID 000466053200011
Linear and nonlinear rheology and structural relaxation in dense glassy and jammed soft repulsive pNIPAM microgel suspensions
2019; 15 (5): 1038-1052
We present an integrated experimental and quantitative theoretical study of the mechanics of self-crosslinked, slightly charged, repulsive pNIPAM microgel suspensions over a very wide range of concentrations (c) that span the fluid, glassy and putative "soft jammed" regimes. In the glassy regime we measure a linear elastic dynamic shear modulus over 3 decades which follows an apparent power law concentration dependence G' ∼ c5.64, a variation that appears distinct from prior studies of crosslinked ionic microgel suspensions. At very high concentrations there is a sharp crossover to a nearly linear growth of the modulus. To theoretically understand these observations, we formulate an approach to address all three regimes within a single conceptual Brownian dynamics framework. A minimalist single particle description is constructed that allows microgel size to vary with concentration due to steric de-swelling effects. Using a Hertzian repulsion interparticle potential and a suite of statistical mechanical theories, quantitative predictions under quiescent conditions of microgel collective structure, dynamic localization length, elastic modulus, and the structural relaxation time are made. Based on a constant inter-particle repulsion strength parameter which is determined by requiring the theory to reproduce the linear elastic shear modulus over the entire concentration regime, we demonstrate good agreement between theory and experiment. Testable predictions are then made. We also measured nonlinear rheological properties with a focus on the yield stress and strain. A theoretical analysis with no adjustable parameters predicts how the quiescent structural relaxation time changes under deformation, and how the yield stress and strain change as a function of concentration. Reasonable agreement with our observations is obtained. To the best of our knowledge, this is the first attempt to quantitatively understand structure, quiescent relaxation and shear elasticity, and nonlinear yielding of dense microgel suspensions using microscopic force based theoretical methods that include activated hopping processes. We expect our approach will be useful for other soft polymeric particle suspensions in the core-shell family.
View details for DOI 10.1039/c8sm02014k
View details for Web of Science ID 000457540000019
View details for PubMedID 30657517
Variational aspects of the Klein-Gordon equation
INDIAN JOURNAL OF PHYSICS
2015; 89 (2): 181-187
View details for DOI 10.1007/s12648-014-0506-6
View details for Web of Science ID 000351564600011