Where the linearized Poisson-Boltzmann cell model fails: (I) spurious phase separation in charged colloidal suspensions

We perform a linearization of the Poisson-Boltzmann (PB) density functional for spherical Wigner-Seitz cells that yields Debye-H\"uckel-like equations agreeing asymptotically with the PB results in the weak-coupling (high-temperature) limit. Both the canonical (fixed number of microions) as well as the semi-grand-canonical (in contact with an infinite salt reservoir) cases are considered and discussed in a unified linearized framework. In the canonical case, for sufficiently large colloidal charges the linearized theory predicts the occurrence of a thermodynamical instability with an associated phase separation of the homogeneous suspension into dilute (gas) and dense (liquid) phases. In the semi-grand-canonical case it is predicted that the isothermal compressibility and the osmotic-pressure difference between the colloidal suspension and the salt reservoir become negative in the low-temperature, high-surface charge or infinite-dilution (of polyions) limits. As already pointed out in the literature for the latter case, these features are in disagreement with the exact nonlinear PB solution inside a Wigner-Seitz cell and are thus artifacts of the linearization. By using explicitly gauge-invariant forms of the electrostatic potential we show that these artifacts, although thermodynamically consistent with quadratic expansions of the nonlinear functional and osmotic pressure, may be traced back to the non-fulfillment of the underlying assumptions of the linearization.Comment: 32 pages, 3 PostScript figures, submitted to J. Chem. Phy

Many-body interactions and melting of colloidal crystals

We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions between the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids. Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pair-interaction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions

The osmotic pressure of charged colloidal suspensions: A unified approach to linearized Poisson-Boltzmann theory

We study theoretically the osmotic pressure of a suspension of charged objects (e.g., colloids, polyelectrolytes, clay platelets, etc.) dialyzed against an electrolyte solution using the cell model and linear Poisson-Boltzmann (PB) theory. From the volume derivative of the grand potential functional of linear theory we obtain two novel expressions for the osmotic pressure in terms of the potential- or ion-profiles, neither of which coincides with the expression known from nonlinear PB theory, namely, the density of microions at the cell boundary. We show that the range of validity of linearization depends strongly on the linearization point and proof that expansion about the selfconsistently determined average potential is optimal in several respects. For instance, screening inside the suspension is automatically described by the actual ionic strength, resulting in the correct asymptotics at high colloid concentration. Together with the analytical solution of the linear PB equation for cell models of arbitrary dimension and electrolyte composition explicit and very general formulas for the osmotic pressure ensue. A comparison with nonlinear PB theory is provided. Our analysis also shows that whether or not linear theory predicts a phase separation depends crucially on the precise definition of the pressure, showing that an improper choice could predict an artificial phase separation in systems as important as DNA in physiological salt solution.Comment: 16 pages, 5 figures, REVTeX4 styl

Models of HoTT and the Constructive View of Theories

Homotopy Type theory and its Model theory provide a novel formal semantic framework for representing scientific theories. This framework supports a constructive view of theories according to which a theory is essentially characterised by its methods. The constructive view of theories was earlier defended by Ernest Nagel and a number of other philosophers of the past but available logical means did not allow these people to build formal representational frameworks that implement this view

A new research agenda for managing socio-cultural integration

Post-acquisition socio-cultural integration has received increasing attention from both scholars and practitioners since the early 1990s. During the past decade, research has increasingly focused on emotions and identity in mergers and acquisitions. This chapter introduces the reader to the vibrant research field and its relevance. This section sets the scene for the book, which provides a deeper understanding of how emotions—both positive and negative—as well as values and identity enable a deeper socio-cultural integration after a merger or acquisition, and how leadership plays a crucial role in making it all happen. This chapter also highlights how the Nordic approach to post-acquisition socio-cultural integration refers to a large community of Nordic academics focusing on the softer social and human side of acquisition, often relying on a huge variety of qualitative methods, and to Nordic companies that are not afraid of adopting a more collaborative approach to post-acquisition integration

Combinatorial design of textured mechanical metamaterials

Biological and Soft Matter Physic

Trans-specialization understanding in international technology alliances: The influence of cultural distance

In the information age, the firm's performance hinges on combining partners' specialist knowledge to achieve value co-creation. Combining knowledge from different specialties could be a costly process in the international technology alliances (ITAs) context. We argue that the combination of different specializations requires the development of "trans-specialization understanding" (TSU) instead of the internalization of partners' specialist knowledge. This article examines the extent to which inter-firm governance in ITAs shapes TSU, and whether the development of TSU is endangered by cultural distance. We hypothesize that relational governance, product modularity, and cultural distance influence TSU development, which in turn influences firm performance. We collected data from 110 non-equity ITAs between software and hardware firms participating in the mobile device sector. We analyzed the data using partial least squares path modeling. Our findings suggest that TSU largely depends on product modularity and relational governance in alliances. However, while cultural distance negatively moderates the path from relational governance to TSU, it has no effect on the relationship between product modularity and TSU. Based on this, we conclude that product modularity can substitute for relational governance when strong relational norms are not well-developed in international alliances. Thus cultural distance does not invariably amount to a liability in ITAs

General Synthetic Domain Theory - A Logical Approach

Synthetic Domain Theory (SDT) is a version of Domain Theory where "all functions are continuous". In [14, 12] there has been developed a logical and axiomatic version of SDT which is special in the sense that it captures the essence of Domain Theory `a la Scott but rules out other important notions of domain. In this article we will give a logical and axiomatic account of General Synthetic Domain Theory (GSDT) aiming to grasp the structure common to all notions of domain as advocated by various authors. As in [14, 12] the underlying logic is a sufficiently expressive version of constructive type theory. We start with a few basic axioms giving rise to a core theory on top of which we study various notions of predomains as well-complete and replete S-spaces [9], define the appropriate notion of domain and verify the usual induction principles.